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Extra resources for Contrôle optimal et jeux différentiels
Both algorithms use the same mechanism of resource distribution whereby order sizes are adjusted to comply with adjusted output plans. We show that the alternative resource distribution algorithm, which distributes resources in proportion to demand, can cause a limit cycle in the sequence of normalized outputs. We consider mechanisms used by sectors to agree on estimates of the expansion rate, which are necessary when planning production. In models of economic systems that use centralized management, there are no (formally, at least) fundamental obstacles for transition to balanced growth (Razumikhin 1974).
T/ must form the left Frobenius vector of A for all t. , in the model considered in Sect. 2). We perform this comparison for the same trajectory of outputs that corresponds to the balanced growth mode. t/) are assumed to be the same in both equations. t/. t C 1/: j;k2Ni j ¤k As we can see, when all other conditions are equal, switching to the personalized prices leads to an increase in profit for a given sector if the sector sells its product to at least two consumers. The reason for this is that the absolute value of the amounts of the discounts decreases.
The distinctive property of the model under consideration is that here personalized discounts are offered for products sold at the average prices. 40) where the first summand equals the amount calculated using the average price and the second summand equals the amount of the additional discount. Here, the first amount depends on the order size linearly, whereas the second amount depends on the same parameter exponentially. t/ < 0 is set individually by each sector and, generally speaking, can be different in different time periods.